Copulas are widely used to specify multivariate distributions
for the statistical modeling of data.
Fields where copula models have had a significant impact include
(but are not limited to) actuarial science [1]}, finance [2]}, [3]}, [4]}, hydrology [5]}, [6]}, climatology [7]},
transportation [8]}, [9]} and marketing [10]}, [11]}.
Copula models are popular because they simplify the specification of a distribution, allowing
the marginals to
be modeled arbitrarily, and then combined using a copula function. In practice,
a major challenge is the selection and estimation of
a copula function that captures the dependence structure well and is tractable.
One choice are
“implicit copulas”, which are copulas constructed from existing multivariate distributions by the
inversion of Sklar's theorem as in [12]}.
This is a large and flexible family of copulas, which
share an auxiliary representation that makes estimation tractable in high dimensions.
Thus, they are suitable for modeling the large datasets that arise in many
modern applications.
The objective of this paper
is to introduce and survey implicit copulas and their use in statistical modeling in an accessible manner.
